I find myself having no trouble with damaging units with shields or barriers but it seems taking out targets with a bar of Armor is a grueling and sometime deadly process (for me). There has to be a weapon/mod or combination of biotics/weapons or combination of biotics someone has discovered that is aggressively devastating to units with armor. I am looking for combinations that work in Multiplayer as well, not just Single Player.

This answer requires more experience then anything. I guess when I say difficult with these opponents I should include that I play silver and gold. Strategy/teamwork is required. I'm looking to attempt a team that can drop all these boss units without spending to much time as the little guys inch their way forward.

7 Answers
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Anything that burns targets works well; Incendiary Ammo and Incinerate weaken armor well and work on most targets. Cryo Ammo claims to weaken armor but that's only on chilled or frozen targets, and most targets that use armor instead of Health don't freeze, and they can be hard or impossible to even chill. Brutes/Banshees for example don't appear to ever be chilled.

Warp effects can help if you're a Biotic, as it also degrades armor. Most Biotic powers don't work very well otherwise, though Singularity does wonders if the target can actually be lifted; many armored targets can't.

For weapons, equipping the Piercing Mod and the Damage Boost mod both help; the piercing mod does more damage to armored targets.

Sniper Rifles work well, generally anything that does it's damage in one single shot works well, so Heavy Pistols can also do the trick. SMG/Assault Rifles don't work very well, and Shotguns don't seem that great.

I believe you mean when all else fails, use fire
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Ben BrockaMar 14 '12 at 13:50

incendiary Ammo is useful in multiplayer IF you have the equipment to constanly have it up. Unfortunately this is not true and so i am struggling to find a combination that i feel definately helps me rid of the pesky atlas/brute/ravanger/pyro/prime/banshees etc.
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ParalyticMar 14 '12 at 13:55

Represented by a yellow bar, armor is one of the less common forms of protection used by enemies. It is likely to be found on higher tier
infantry, commander units and bosses. It is used in some regard by all
factions and provides a strong layer of protection for most foes.
Armor is best countered by weapons that fire single powerful rounds as
opposed to numerous weak ones. Therefore, against any armored
opponent, it is advisable that selected individuals have either a
Shotgun or Sniper Rifle. Heavy Pistols, which are semi automatic and
fire large bullets, are less effective at taking down armor than
shotguns or sniper rifles but more effective at it than an Assault
Rifle or Submachine Guns.

Armor can be countered by a variety of powers. Combat powers are
probably the least effective with the exception of Adrenaline Rush.
The best tech power against armor is Incinerate as fire is one of
armor's greatest weaknesses. Biotic powers are less useful against
armor but Warp still presents an option for degrading the armor of an
opponent. Incendiary Ammo and Warp Ammo also helps.

I agree with everything 'CaulynDarr' posted, except for the biotic part. Detonations such as warp+throw works realy well against banshees and brutes on insanity (warp itself deals damage to armors and "detonation-throw" just makes fun of them). This is especialy true if u have power damage bonus from glyph, your own armor and squadmates (passives such as garrus in rank 6 grant you 10% power damage).

Tech powers: incinerate (as stated above)

Amo powers: Armor piercing ammo (75%dm) is actually the best against it, but if your going with a class with no ammo powers (adept/engeneer) i'd go for the warp (68% dm arm and health, 88%dmg to barriers - best ammo power of me3). Incendiary ammo is also nice.

Weapons: sniper vs pistol. If you're infiltrator/soldier go for the sniper as your main sorce of damage aginst armors. If your character is not much into guns, a good way to deal power damage is the pistol. Rank 5 paladin+vindicator+locust wth ultra light materials let's you keep aprox 200 cooldowns and still let's you deal with everything. Equip avnger/vindicator with your ammo power of choice, the smg with either warp ammo(bonus power) or squad-shreder ammo (from ashe) and the pistol with warp/squad armor piercing+piercing mod. This means that the pistol will serve essencially teh role of armor destruction since it's power is considerably nerfed from the piercing mod.

I've made 3 playthroughs on insanity and this is what i find to be most usefull. Just my opinion though, hope it helps ;)